Non-contact topographical analysis apparatus and method thereof

ABSTRACT

Topographic analysis apparatus consists of a light source ( 1 ) and associated optics ( 2 ) for illuminating a mirrored surface O with a parallel light beam. Light reflected from the mirrored surface is collected by a camera ( 4 ) that is mounted on a moveable carriage ( 5 ) so that images of the mirrored surface O may be recorded at a plurality of different distances from the surface. The Makyoh topograms produced using this apparatus are then analyzed using phase extraction software to iteratively determine the profile of the surface of the object and the object&#39;s reflectivity. In this way Makyoh topograms may be used for quantitative as well as qualitative analysis of a reflective surface such as a semiconductor wafer.

FIELD OF THE INVENTION

The present invention relates to non-contact topographical analysisapparatus and a method thereof and in particular to the generation ofMakyoh topograms enabling quantitative measurement of variations in themirrored surface of an object. The present invention is particularlyconcerned, but not exclusively, with the simultaneous measurement of thereflectivity and height variations of a large mirror-polished surface,such as defects in semiconductor wafer surfaces.

BACKGROUND OF THE INVENTION

For the current generation of microelectronic circuits, themanufacturing process requires perfectly flat large diametersemiconductor wafers. There is a well-defined need for characterisationtechniques that can accurately assess the polishing quality of thesewafers and can be used as quality control and production line monitoringtools providing qualitative pass/fail type information and also astroubleshooting tools providing detailed and accurate quantitativeinformation.

It has been known for some time that when a collimated beam of light isreflected by an approximately flat mirror-polished object and a screenis placed in the path of the reflected beam some distance away from theobject, a ‘mirror image’ of the object is formed on the screen. For aperfectly flat object with uniform reflectivity, the light intensity inthe ‘mirror image’ would be substantially uniform with some smallvariations due to edge diffraction effects close to the perimeter of theobject. However, for objects with surface height variations, the ‘mirrorimage’ no longer has a uniform intensity distribution. Even small heightvariations in the surface of the object will show up strongly amplifiedas dark or bright patches/lines in the ‘mirror image’. ‘Mirror images’of this type are called Makyoh topograms or ‘magic mirror images’.Makyoh topography has been used for a number of years as a tool for theinspection of mirror-polished surfaces, and in particular as a qualitycontrol tool for the assessment of semiconductor wafer surfaces.

In FIG. 1 a conventional Makyoh topograph is shown schematically. Lightfrom a laser 1, or a bright lamp with a narrow bandpass filter, ishomogenised using a diffuser, fly's eye optics, or spatial filterassembly 2. A collimator lens 3 then forms an approximately parallellight beam, which in turn is reflected by the object 0 under test. Thereflected beam is intersected either by a screen 4 for direct viewing orby a film or electronic camera for image recording. The object-cameradistance is fixed and normally is in the range of 0.5 m to 2 m.

Typical Makyoh topograms from three different mirror-polished InP wafersare shown in FIGS. 2a, 2 b and 2 c. In FIG. 2a the image contrast israther complex with the following main components: curved approximatelyparallel lines probably corresponding to saw or lapping marks;concentric circles in the centre of the image probably corresponding togrowth striation lines; dark lines with cellular geometry probablycorresponding to surface ridges caused by uneven mounting waxdistribution during polishing; and dark and bright spots probablycorresponding to mounds and dimples respectively. The wafer shown inFIG. 2b is of better overall quality, the only features revealed in thetopogram are concentric circles in the centre and a small number ofbright spots at random positions. Finally, the wafer shown in FIG. 2c isof excellent quality only exhibiting some very faint low contrast linesand spots. These images provide a qualitative measure of wafer polishingquality, however it is not possible to extract the actual height of theridge network revealed in FIG. 2a or the depth of the dimples in FIG.2b. As demonstrated by these images, conventional Makyoh topograms canbe a very powerful tool for qualitative comparison, but they provide noquantitative information and the interpretation of the image contrastcan be very complicated.

U.S. Pat. No. 4,547,073 describes apparatus for generating Makyohtopograms that includes a convex lens for converging light reflectedfrom the object in order to project a defocussed image on the screen.With the apparatus described in U.S. Pat. No. 4,547,073 the distancebetween the object and the screen is reduced, in comparison to apparatusthat does not employ a convex lens thereby making the apparatus moreconvenient for industrial use. A geometrical optics explanation isprovided as to how the variations in surface height result in changes inintensity in the mirror image. However, the explanation is very generalrelying as it does on equating variations in surface height solely to aconcave/convex mirror effect. This document provides no assistance as tohow a quantitative analysis of the Makyoh topograms might be achieved.

The main drawbacks of Makyoh topography as described above are:Ambiguity in the interpretation of the topograms: almost identicalMakyoh topograms can result from an object with some given surfaceheight profile and constant reflectivity; an object with constantsurface height and a given non-uniform reflective or an object with bothheight variations and a non-uniform reflectivity profile.

Lack of quantitative interpretation of the topograms.

SUMMARY OF THE INVENTION

The present invention seeks to provide improved topographical analysisapparatus and a method thereof that at least improves and in many casesovercomes the disadvantages described above with conventional Makyohtopography and in particular enables a quantitative interpretation ofMakyoh topograms generated with the present invention.

The present invention provides a topographical analysis method formeasuring variations in reflectivity or surface height of a reflectiveobject comprising: illuminating a reflective surface of the object witha beam of light; recording with a recording device a plurality of imagesof the surface of the object generated by light reflected from thesurface in which each image has a predetermined optical transformationwith respect to every other image; measuring the light intensitydistribution in each of the images generated by the reflected light; anddetermining and outputting at least one of the reflectivity and therelative surface height of the reflective surface of the object bypredicting the reflectivity and relative surface height of an initialtheoretical surface, iteratively adjusting the theoretical surface untilthe calculated light intensity distributions for the theoreticalsurface, corresponding to the optical transformations of each of therecorded images, converge with the recorded images.

Preferably the theoretical surface is adjusted by cyclical substitutionof the calculated image intensity for the theoretical surface with thedetected image intensity of each one of the images generated by thereflected light. In the preferred embodiment the light distribution ofthe theoretical surface is deemed to have converged when the differencebetween the calculated image intensity and the detected imageintensities is less than a predetermined threshold.

In one embodiment of the present invention the plurality of images arerecorded each at a different distance from the reflective surface of theobject. The recording device may be moved to different positions alongthe optical axis of the reflected light to sequentially record theplurality of images. Alternatively, the reflected light may be dividedinto a plurality of portions with each portion of the reflected lightbeing directed to a separate recording device in which the path lengthfrom the reflected surface of the object to each recording device isdifferent. In a further alternative the effective path length betweenthe object and the recording device may be altered by adjusting anyoptical elements located between the object and the recording device.

In a further or alternative embodiment the image generated by thereflected light is recorded at a plurality of different, distinctwavelengths. Additional optical elements may be provided for modifying(e.g. collimating) the incident beam of light. Where such additionalelements are provided, the elements may be adjustable to enable theplurality of images each with a different optical transformation to begenerated.

In a second aspect the present invention provides topographical analysisapparatus for measuring variations in the reflectivity or surface heightof a reflective object comprising an optical system for directing a beamof light to a reflective surface of the object; a first recording devicefor recording a first image of the surface of the object generated bylight reflected from the surface; at least one further recording devicefor recording one or more further images of the surface of the object,thereby generating a plurality of images in which each image has apredetermined optical transformation with respect to every other image:and an analyser for measuring the light intensity distribution in eachof the plurality of images and for determining and outputting at leastone of the reflectivity and the relative surface height of thereflective surface of the object by iteratively adjusting a theoreticalsurface, having an initial predetermined reflectivity and surfaceheight, until the calculated light intensity distributions for thetheoretical surface, corresponding to the optical transformations ofeach of the recorded images, converge with the recorded images.

Ideally, the analyser further includes a thresholding device formonitoring the difference between the calculated image intensity of thetheoretical surface and the recorded image intensities and fordetermining that the theoretical surface substantially corresponds tothe surface of the reflective object when the difference is less than apredetermined value.

The light source may be one or more narrow band-width sources such aslasers etc. Also, the first and the one or more further recordingdevices may be electronic cameras.

In one embodiment the first recording device and the one or more furtherrecording devices is a single camera mounted on a moveable support forpositioning the camera at different distances from the reflectivesurface of the object.

In a further or alternative embodiment the first and one or more furtherdetector devices are wavelength specific and each is sensitive to adifferent distinct wavelength.

In a further aspect the present invention provides phase extractionsoftware on a data carrier for determining variations in reflectivity orsurface height of a reflective object, the software being programmed toperform the following steps: storing the measured light intensitydistributions of a plurality of images of a reflective object in whicheach image has a predetermined optical transformation with respect toevery other image; predicting the reflectivity and relative surfaceheight of an initial theoretical surface and calculating the lightintensity distribution for the theoretical surface; and iterativelyadjusting the theoretical surface until the calculated light intensitydistributions for the adjusted theoretical surface, corresponding tooptical transformations of the stored images, converge with the storedlight intensity distributions.

With the present invention, optical apparatus is provided for therecordal of more than one Makyoh topogram from the same object. Thetopograms are generated in such a way that the light intensitydistributions resulting in the different topograms are subject towell-defined and different optical transformations (e.g. phasedispersion) on travelling from the object to the recording device. Thequantitative interpretation of a set of such topograms then becomes aphase retrieval problem that can be solved using iterative numericalalgorithms. With the present invention iterative Fourier transformtechniques are employed that, where possible, are used to obtain aunique solution for the object reflectivity and surface height (phase)distributions.

Embodiments of the present invention will now be described, by way ofexample, with reference to the accompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a conventional Makyoh topograph;

FIGS. 2a. 2 b and 2 c are conventional Makyoh topograms from threedifferent mirror-polished InP wafers;

FIGS. 3a and 3 b are diagrams of a test object surface in which thereflectivity (FIG. 3a) is constant but the phase (FIG. 3b) varies byvirtue of four surface dimples;

FIGS. 4a and 4 b are diagrams of the calculated Makyoh topogramsgenerated for the test object of FIGS. 3a and 3 b at an object/cameraseparation of 1m (FIG. 4a) and 2m (FIG. 4b);

FIGS. 5a and 5 b are diagrams of the reflectivity and phase respectivelyof a reconstructed object surface based on the topograms of FIGS. 4a and4 b;

FIGS. 6a, 6 b, 6 c and 6 d are line traces taken from the surfaces ofFIGS. 3a, 3 b, 5 a and 5 b that run respectively through the fourreconstructed dimples;

FIG. 7 is a schematic diagram of a topographical analysis apparatus inaccordance with the present invention;

FIG. 8 is a schematic diagram of alternative topographical analysisapparatus in accordance with the present invention;

FIG. 9 is a schematic diagram of a third embodiment of topographicalanalysis apparatus in accordance with the present invention;

FIG. 10 is a Makyoh topogram of a sample InP wafer;

FIG. 11 is a series of reconstructed Makyoh topograms converging on thetopogram of FIG. 10; and

FIG. 12 is a three dimension diagram of the calculated surface profileof the surface of the wafer of FIG. 10.

DETAILED DESCRIPTION OF THE DRAWINGS

As mentioned above conventional Makyoh topographs and their explanationin terms of geometrical optics fails to provide any quantitative measureof the variations in surface height. In order to determine the exactvalues of intensity as a function of lateral position, diffractioneffects have to be taken into account. In the paraxial, coherent regime(which is a valid approximation for the optical systems considered here)the following simplified treatment can be employed. For the light beamreflected by the mirror and for an axial position immediately next toit, the complex amplitude distribution α_(m)(x,y) can be calculated byapplying an operator P to the mirror reflectivity r(x,y) and the mirrorsurface height h(x,y), i.e. α_(m)(x,y)=P{r(x,y),h(x,y)}. In thisnotation the operator P is a function of the wavelength λ and thewavefront α₀(x,y) incident on the mirror. If α₀ is a constant plane wavewith magnitude u₀ and wavelength λ and the mirror surface is smooth,α_(m)=P{r,h} takes the simple form of:

α_(m) =u ₀ r(x,y)e ^(−i2πh(x,y)λ)

Here the wavefront tilt caused by the non-perpendicular angle ofincidence was ignored; this however does not effect the generality ofthe treatment. The complex amplitude distribution α_(i(x) _(i),y,_(i))at the camera can then be calculated by applying the free-space phasedispersion operator to α_(m). In the Fourier domain this takes the formF{α_(i)}=HF{α_(m)}. For the geometry considered here, H is amultiplication by the factor ^(−πλ  z(f_(x)² − f_(y)²))

where z is the distance between the mirror-polished surface and thecamera and f_(x) and f_(y) are the Fourier-space co-ordinates, givingfor α_(i) the expression: $\begin{matrix}{a_{i} = {F^{- 1}{\left\{ {^{{- {\pi\lambda}}\quad {z{({f_{x}^{2} + f_{y}^{2}})}}}F\left\{ {u_{0}{r\left( {x,y} \right)}^{{- {2\pi}}\quad {{h{({x,y})}}/\lambda}}} \right\}} \right\}.}}} & (1)\end{matrix}$

The image intensity I_(i) can then be calculated by taking the squaremodulus of α_(i), i.e. I_(i)=Iα_(i)I².

As proof of the validity of the above equation, a test mirror object(FIGS. 3a and 3 b) was assumed with constant r=1.0 reflectivity (FIG.3a) and a flat surface with four dimples {fraction (1/100)}, {fraction(1/50)}, {fraction (1/20)} and {fraction (1/10)}λ deep (marked A, B, Cand D respectively in FIG. 3b). The phase is inversely proportional tothe object surface height and so the dimples A, B, C and D are shown asbright spots in FIG. 3b. Using the analysis set out above, two Makyohimages were calculated for the test object for object-to-screendistances of z=1 m (FIG. 4a) and z=2 m (FIG. 4b). The similarity betweenthese calculated images and actual Makyoh topograms produced usingconventional topographs is remarkable and confirms the validity of thisapproach to a quantitative measurement of Makyoh topograms.

If the illumination were incoherent the above results would not bevalid, however a similar treatment could easily be developed and appliedas necessary.

In order to make Makyoh topography quantitative the functions r(x,y) andh(x,y) would need to be recovered from a measured I_(i)(x_(i),y_(i)). Ifthe phase of Makyoh images was available, the process represented by Eq.(1) could be inverted and the object reflectivity and phase (height)could be recovered. However, since only intensity can be measured. thephase information is lost. On the basis of a single Makyoh topogramEq.(1) cannot be inverted and a unique quantitative solution for r(x.y)and h(x,y) cannot be obtained.

As mentioned above, this problem is a phase retrieval problem thatarises when trying to determine r(x,y) and h(x,y) from intensitymeasurements. Using the topograhical analysis method and apparatus andassociated phase extraction software described below. at least twoseparate images generated by the reflected light are recorded and thelight intensity distribution of the images measured. A theoreticalsurface with a predetermined reflectivity and surface height profile isassumed and using phase retrieval software is iteratively adjusted.using the algorithm set out below, so that the calculated imageintensities of the theoretical surface converge on the recorded imageintensities under the same parameters. Once the differences between thecalculated image intensities and the recorded image intensities are lessthan a threshold value. the theoretical surface is deemed to be anaccurate representation of the actual surface under study. Anexplanation of how such an iterative approach is implemented in practiceis set out below.

Eq. (1) for the complex image amplitude can be presented in thefollowing general form:

α_(i) =F ¹ HFP{r(x,y h(x,y)}  (2)

where P is a function of the illumination complex amplitude α₀ and thewavelength λ and H is a function of the distance z between the objectand the camera and the wavelength λ. Applying the inverse of Eq. (2) toα_(i), r and h can be found as

r(x,y)=F ¹ H ¹ FP _(r) ⁻¹{α_(i)}

and

h(x,y)=F ¹ H ¹ FP _(h) ⁻¹{α_(i)}.

The notation can be simplified by defining a composite operator C as

C=F ¹ HFP, $\begin{matrix}{C_{r}^{- 1} = {F^{1}H^{1}{FP}_{r}^{- 1}\quad {and}}} \\{C_{h}^{- 1} = {F^{1}H^{1}{{FP}_{h}^{- 1}.}}}\end{matrix}$

With this notation the algorithm described above can be applied in theretrieval of phase information from a Makyoh topogram in the followingmanner.

Two Makyoh topograms I_(A) and I_(B) are recorded under two differentsets of imaging conditions having corresponding complex amplitudes α_(A)and α_(B), and imaging operators C_(A) and C_(B). Using the methoddescribed above for the retrieval of phase information from a pair ofimages, the first iteration is performed with an arbitrary phase assumedfor α_(A): $\begin{matrix}{a_{B,1} = {\sqrt{I_{B}}^{\quad {\arg {({C_{B}{\{{C_{A,r}^{- 1}{\{{\sqrt{I_{A}}^{{\varphi}\quad \Omega}}\}}C_{A,h}^{- 1}{\{{\sqrt{I_{A}}^{\iota\varphi\Omega}}\}}}\}}})}}}\quad {and}}} \\{a_{A,1} = {\sqrt{I_{A}}{^{\quad {\arg {({C_{A}{\{{C_{B,r}^{- 1}{\{ a_{B,1}\}}C_{B,h}^{- 1}{\{ a_{B,1}\}}}\}}})}}}.}}}\end{matrix}$

The process is then repeated with values from the previous iteration,$\begin{matrix}{a_{B,{n + 1}} = {\sqrt{I_{B}}{^{\quad {\arg {({C_{B}{\{{C_{A,r}^{- 1}{\{ a_{A,n}\}}C_{A,h}^{- 1}{\{ a_{A,n}\}}}\}}})}}}.}}} \\{a_{A,{n + 1}} = {\sqrt{I_{A}}{^{\quad {\arg {({C_{A}{\{{C_{B,r}^{- 1}{\{ a_{B,{n + 1}}\}}C_{B,h}^{- 1}{\{ a_{B,{n + 1}}\}}}\}}})}}}.}}}\end{matrix}$

until changes in A_(i) and A_(p) become smaller than a given pre-setlimits or thresholds. Once sufficient convergence is achieved, objectreflectivity and height can be calculated from either α_(A) or α_(B).

If the illumination or image forming optical paths included additionaloptical elements (e.g. lenses) or a somewhat modified geometry was used,the actual form of C and C⁻¹ would be different. However, the generalargument and the algorithm described above would still be applicable ifa) the two measured images I_(A) and I_(B) possessed sufficientreciprocity for the algorithm to converge, b) the inverse operator H⁻¹existed and c) the inverse operator P⁻¹ existed and was separable inrand h.

To test the phase retrieval software described above, it was applied tothe topograms shown in FIGS. 4a and 4 b. The results of thereconstruction are shown in FIGS. 5a and 5 b (c.f. the original objectis shown in FIGS. 3a and 3 b). FIG. 5a shows the reconstructedreflectivity which is constant and FIG. 5b shows the reconstructed phase(height) which varies in the form of four dimples that differ in height.The agreement between the reconstruction and the original test image isfurther illustrated by the line traces shown in FIGS. 6a, 6 b, 6 c and 6d. The traces were selected such that they go through the centre of thedimples in the surface of the test object shown in FIGS. 3a and 3 b. Thesolid line in the line traces correspond to the original surface and thecircles represent data points for the reconstructed surface heightprofile.

Thus, to enable quantitative measurement of the mirror-polished surfaceof an object, two or more independent mirror images of the object withsufficient reciprocity are required. This condition will be satisfied ifone or more of the corresponding constituent pairs of the operator pairC_(A)/C_(B), i.e.H_(A)/H_(B) and P_(A)/P_(B), are sufficientlydifferent. In addition the geometry of the optical arrangement has toensure the existence of the inverse operators required by thereconstruction algorithm referred to above.

Topographical analysis apparatus capable of providing a quantitative aswell as a qualitative measure of variations in reflectivity and phase(surface height) of a mirror-polished object, employing the method setout above is shown in FIG. 7. Many of the features of this apparatusalso appear in the conventional Makyoh topograph shown in FIG. 1 andwhere appropriate the same reference numerals are employed.

The topographical analysis apparatus includes a light source 1 such as alaser or a bright lamp with a narrow band-pass filter for illuminatingthe mirror-polished surface of an object O. The light from the lightsource 1 passes through an optical system that homogenises the light andgenerates a parallel light beam. The optical system may convenientlyconsist of a diffuser, fly's eye optics or spatial filter assembly 3 anda collimator lens. Preferably, the parallel light beam has across-section sufficiently large to illuminate the entire surface of theobject. Alternatively, only a portion of the surface of the object maybe illuminated in which case different parts of the object can beilluminated in turn to enable a complete image of the surface of theobject to be constructed from the individual mirror-images producedusing the topographical analysis apparatus.

Light reflected from the surface of the object is intersected by acamera 4 so that the mirror image can be analysed. The camera may usefilm or may be electronic with a pixellated image frame. The camera 4 ismounted on a moveable support 5 such as a trolley or carriage in movingengagement with guide rails (not shown). The moveable mount 5 isarranged for movement parallel to the reflected light beam so that thecamera 4 may be moved to two or more different positions at differentdistances z from the object. At each of the two or more positions aseparate mirror image of the surface of the object is generated so thatthe quantitative information can be extracted from the plurality ofmirror images. Instead of continuously variable positions, a pluralityof positions of the moveable mount 5 may be predetermined. The camera 4is connected to an analyser that implements the algorithm set out abovefor the extraction of both reflectivity and surface height quantitativedata.

As shown in FIG. 8, instead of the camera 4 having a moveable mount 5, aplurality of fixed cameras 7, 8 may be employed in combination with abeam splitter 9 inserted in the path of the reflected light beam. Theplurality of cameras are each positioned to provide different fixed zvalues. This arrangement has the advantage that simultaneous recordingof a plurality of mirror images by the cameras can be achieved and theimages supplied to the analyser 6. In a further alternative, if theobject-to-screen optical path includes additional optical elements, saylenses, similar effects on H can be achieved by mounting one or more ofthe optical elements on a moveable support.

With each of the embodiments given above, as H is a function of z,different H_(A), H_(B), . . . operators can be obtained for each cameraposition. Assuming the operators to be sufficiently different, thereconstruction algorithm can be employed by the analyser 6 toiteratively extract phase information from the plurality ofsubstantially independent mirror images.

Instead of varying the object to camera distance z, the complexamplitude distribution of illumination may be varied to again produce aplurality of substantially independent mirror images. This can mostconveniently be achieved by mounting the collimator lens 3 on a moveablesupport (not shown) so that the collimator lens 3 may be moved todifferent positions along the optic axis. In this way different P_(A),P_(B), . . . operators can be obtained.

Since both H and P are functions of the illumination wavelength λ, ifprovisions are made for illumination at two or more wavelengths and forindependent image recording at those wavelengths (for example by meansof a colour camera) different C_(A), C_(B), . . . operators can beobtained. An example for this type of system is shown in FIG. 9. Thetopographic analysis apparatus includes, as for the previousembodiments, a spatial filter 2 and a collimator lens 3 for directing aparallel beam of light onto the surface of the object O. A camera 4 ispositioned in the optic axis of the reflected light to produce a mirrorimage of the object surface. The camera 4 may be a conventional film ordigital camera, capable of recording images at a broad range ofwavelengths. In which case the beam of light incident on the object iswavelength specific and one or more further mirror images aresuccessively generated each at a different wavelength. To ensure theincident beam of light is wavelength specific, the light source may be atuneable narrow band laser or alternatively a plurality of lasers eachgenerating light at different frequencies that are sequentially alignedwith the optical axis of the apparatus.

If a colour specific camera is employed, then the object may beilluminated with light at a plurality of distinct wavelengths and aplurality of successive mirror images may again be obtained at thedifferent wavelengths. Of course, a beam splitter may be employed in themanner shown in FIG. 8 to enable two mirror images at differentwavelengths to be generated simultaneously.

In addition, any combination of the above arrangements may also be used.For example, a plurality of images can be recorded at differentwavelengths and at different positions by combining the arrangements ofFIGS. 7 and 9.

The apparatus in FIG. 9 is preferred as both H and P are varied. Also,where more than two independent mirror images are generated, therobustness and convergence speed of the reconstruction algorithm may besignificantly improved.

The apparatus shown in FIG. 7 was used to take a series of Makyohtopograms of a sample semiconductor wafer, one of which is shown in FIG.10. The dark regions marked m indicate where the mounting wedges forholding the wafer are positioned. The sample was a polished 50 mmdiameter InP wafer and the topogram of FIG. 10 was recorded at an imageto object distance of 656.6 mm. Additional topograms were recordedcloser to the object. The image contrast is complex consisting ofconcentric circles in the center of the wafer, irregular large dark andbright patches and a pronounced cellular network of dark lines withbright spots in the centre region of the cells. The phase extractionsoftware described above was applied starting with an initial randomimage phase (i=0). After only approximately 100 iterations (i=100) therate of change for the reconstructed images decreased significantly andfinally the process was stopped after 300 iterations when no furtherchanges were observed even in the fine detail of the reconstructedimages. From the measured intensities of the reconstructed topogramphases the object reflectivity and phase shift were then calculated. Theobject reflectivity was found to be close to unity for the whole waferbut the object was found to introduce significant phase shifts. Havingreconstructed the phase shift, reconstruction of the object heightprofile was straightforward.

The present invention provides a number of advantages over theconventional Makyoh topography. Firstly, interpretation of the recordedtopograms is unambiguous and provides quantitative data with highsensitivity. Also, both object reflectivity and height measurements areprovided. Moreover, the topographic apparatus is simple in constructionand affords a wider range of applicability when compared to conventionalMakyoh topography. It will of course be apparent that the phaseextraction software may be used separately from the apparatus describedabove where appropriate Makyoh topograms of a reflective object areprovided for analysis.

The simplicity of the topographic apparatus makes it suitable forretrofitting to existing conventional systems. For example a beamsplitter and a second camera at a different height can be added to anexisting Makyoh topograph. Alternatively, a beam splitter and a secondcamera can be used in combination with mirrors to lengthen the opticalpath of a portion of the reflected light. Indeed, all of the embodimentsdescribed above can be implemented with existing conventional apparatus.

Although reference has been made herein to the use of the presentinvention to quantitatively measure the mirror-polished surface of awafer, it will be appreciated that the present invention may be employedin many different situation where near perfect mirror surfaces arerequired. For example, the invention may be used to monitor the qualityof mirrors used in communications and with lasers.

What is claimed is:
 1. A topographical analysis method for measuringvariations in reflectivity or surface height of a reflective objectcomprising: illuminating a reflective surface of the object with a beamof light; recording with a recording device a plurality of images of thesurface of the object generated by light reflected from the surface inwhich each image has a predetermined optical transformation with respectto every other image; measuring the light intensity distribution in eachof the images generated by the reflected light; and determining andoutputting at least one of the reflectivity and the relative surfaceheight of the reflective surface of the object by predicting thereflectivity and relative surface height of an initial theoreticalsurface, iteratively adjusting the theoretical surface until thecalculated light intensity distributions for the theoretical surface,corresponding to the optical transformations of each of the recordedimages, converge with the recorded images.
 2. A method as claimed inclaim 1, wherein the theoretical surface is adjusted by substitution ofthe calculated image intensity for the theoretical surface with thedetected image intensity of one of the images generated by the reflectedlight.
 3. A method as claimed in claim 2, wherein the detected imageintensity of each of the plurality of images is sequentially substitutedfor the calculated image intensity of the theoretical surface.
 4. Amethod as claimed in claim 3, wherein the light intensity distributionof the theoretical surface is deemed to have converged when thedifference between the calculated image intensity and the detected imageintensities is less than a predetermined threshold.
 5. A method asclaimed in claim 1 wherein the plurality of images are recorded each ata different distance from the reflective surface of the object.
 6. Amethod as claimed in 5, wherein the recording device is moved todifferent positions along the optical axis of the reflected light tosequentially record the plurality of images.
 7. A method as claimed in5, comprising the further step of dividing the reflected light into aplurality of portions and directing each portion of the reflected lightto a separate recording device in which the path length from thereflected surface of the object to each recording device is different.8. A method as claimed in claim 7, wherein the effective path length ofthe reflected light is altered by adjustment of optical elements locatedbetween the object and the recording devices.
 9. A method as claimed inclaim 1, further comprising the step of modifying a beam of light anddirecting the modified beam to the reflective surface of the object bymeans of an adjustable optical system, wherein the adjustable opticalsystem is changed between each image recording.
 10. A method as claimedin claim 1, wherein the image generated by the reflected light isrecorded at a plurality of different, distinct wavelengths. 11.Topographical analysis apparatus for measuring variations in thereflectivity or surface height of a reflective object comprising anoptical system for directing a beam of light to a reflective surface ofthe object; a first recording device for recording a first image of thesurface of the object generated by light reflected from the surface; atleast one further recording device for recording one or more furtherimages of the surface of the object, thereby generating a plurality ofimages in which each image has a predetermined optical transformationwith respect to every other image; and an analyser for measuring thelight intensity distribution in each of the plurality of images and fordetermining and outputting at least one of the reflectivity and therelative surface height of the reflective surface of the object byiteratively adjusting a theoretical surface, having an initialpredetermined reflectivity and surface height, until the calculatedlight intensity distributions for the theoretical surface, correspondingto the optical transformations of each of the recorded images, convergewith the recorded images.
 12. Topographical analysis apparatus asclaimed in claim 11, wherein the analyser further includes athresholding device for monitoring the difference between the calculatedimage intensity of the theoretical surface and the recorded imageintensities and for determining that the theoretical surfacesubstantially corresponds to the surface of the reflective object whenthe difference is less than a predetermined value.
 13. Topographicalanalysis apparatus as claimed in claim 11, wherein there is furtherprovided a light source.
 14. Topographical analysis apparatus as claimedin claim 13, wherein the light source has a narrow band-width. 15.Topographical analysis apparatus as claimed in claim 11, wherein therecording apparatus comprises a plurality of recording devices beingelectronic cameras.
 16. Topographical analysis apparatus as claimed inclaim 15,wherein the plurality of detector devices is wavelengthspecific and each is sensitive to a different distinct wavelength. 17.Topographical analysis apparatus as claimed in claim 16, furtherincluding a plurality of wavelength specific light sources. 18.Topographical analysis apparatus as claimed in any one of claims 11 to15, further including one or more beam splitters for dividing thereflected light into a plurality of portions and for directing eachportion to a different detector device.
 19. Topographical analysisapparatus as claimed in claim 11, wherein the recording apparatus deviceis a single camera mounted on a moveable support for positioning thecamera at different distances from the reflective surface of the object.20. Topographical analysis apparatus as claimed in claim 11, wherein oneor more adjustable optical elements are provided between the object andthe recording apparatus, the optical elements being mounted on a movablesupport so as to alter the effective path length of the reflected light.21. Topographical analysis apparatus as claimed in claim 11, wherein anadjustable optical system is provided between the light source and theobject, one or more elements of the optical system being mounted on amoveable support so as to modify the illuminating beam of light.
 22. Amethod of adjusting a Makyoh topograph to enable quantitativemeasurement of the surface of a reflective object comprising introducingplural imaging means for enabling one or more further Makyoh topogramsto be detected each having a different optical transformation withrespect to every other topogram; measuring the light intensitydistribution in each of the topograms generated by the reflected light;and determining at least one of the reflectivity and the relativesurface height of the reflective surface of the object by predicting thereflectivity and relative surface height of an initial theoreticalsurface, iteratively adjusting the theoretical surface until thetheoretical light intensity distributions for the theoretical surface,corresponding to the optical transformations of each of the topograms,converge with the topograms.